Formation porosity exploration



23 1966 J. A. WINTER 3,268,858

FORMATION POROS ITY EXPLORATION Filed Feb. 4, 1963 4 Sheets-Sheet 1 CENTER OF GRAVITY AT 50% ARITHMETIC DEVIATION AVERAGE POMS/TY ENERGY LEVEL F" fi\ FIG.I

ENTER OF GRA V/ r Y ARITHME TIC DEVIATION FIG, 2 AVERAGE POROSITY ENERGY LEVEL SEA LEVEL ENTER MOVEMENT OF I OF AV/r SAND BAR 0N ARITHMET|C AVERAGE Poms/TY FIG 3 TRANSGRESSION UNCONFORMITY Aug. 23, 1966 J. A. WINTER FORMATION POROSITY EXPLORATION 4 Sheets-Sheet 2 Filed Feb. 4, 1963 f I l MzEmQZQW 35223 M Q 223 mm 223 mm 223 mm 0 228 mm 223 mm m M mzokmqzqm I 1 I'll/l $855 3 3 5 Q 1 1 I I 1 I I I m l lflMl I -llliilrfii- I- lilllllilllil 220w am 228 mm 223 mm 223 am m Q o m United States Patent O 3,268,858 FORMATION POROSITY EXPLORATION Jan A. Winter, Tulsa, Okla., assignor to Century Geophysical Corporation, Tulsa, Okla., a corporation of Delaware Filed Feb. 4, 1963, Ser. No. 255,760 16 Claims. (Cl. 34015.5)

This invention relates to the production of indicia as to the location of areas favorable to hydrocarbon accumulation and, more particularly, to the evaluation of subterranean trends exhibiting a characteristic porosity function.

The many endeavors to provide an understanding for the character of the earths lithology, the location of anomalous zones within the earths crust, the reasons for the occurrence of such anomalies, and the behavior of such anomalies in connection with the exchange of liquid and solid constituents in the earths formations over large periods of time have led to the development of many and varied tools. Geophysicists and geologists employ every measurement capable of yielding an additional bit of information relating to the lithological character of the earths crust. This is particularly the case in the search for minerals and particularly for deposits of hydrocarbons.

The refinement of exploratory techniques such as radioactivity logging, electrical logging and acoustic logging has provided tools which have been mainly used by geophysicists and reservoir engineers and geologists primarily as a correlation tool. In connection with each of the foregoing types of logging operations, theoretical considerations have led to the determination of a factor or parameter of the earths crust which is of significance. This factor is that of the porosity of the earths formations. Many and varied have been the interpretive techniques applied to the formation dependent data represented by radioactive, electrical and acoustic logs.

The present invention relates to an exploration technique and the development of additional parameters based upon a porosity function for revealing the structural character of the earths formations and particularly those areas and trends in those areas of porous nature which are likely or possibly will contain accumulations of hydrocarbons. More particularly, in accordance with the present invention, there is provided a method of determining the timestructural development of subterranean earth formations. Included in the method are the steps of measuring an earth dependent function of a lithologic body along at least two laterally spaced, vertically directed lines extending to the body of interest. The function is then modified to produce a porosity function of the body. From the porosity function there is then established a numerical value of the deviation from an average of the porosity functions over the thickness of the body at the location of each of the said lines and the deviation function is then registered in correlation with the location of the lines.

In accordance with a further aspect of the invention, a further function is developed, namely, a function representative of the center of gravity of the body. The location of the center of gravity is plotted in correlation with said locations.

In a preferred embodiment of the invention, an incremental acoustic velocity function of a given lithologic body is produced for each of at least two vertically oriented traverses through the body with the porosity function for each of said locations being developed from the incremental acoustic velocity function. From the porosity function the arithmetic deviation of the porosity function over the section is developed along with the deviation from the center of the body of the center of gravity. The latter two functions are then plotted as a function in correlation with the location of the two lines through the body to provide a measure of the movement of characteristic sections of the body in the course of its initial devel opment.

It is to be understood that the invention relates to the application of statistical methods to porosity information available from earth dependent geophysical logs to estab lish a criteria for determination of the origin of given lithologi'c bodies.

For a more complete understanding of the present in vention and for further objects and advantages thereof, reference may now be had to the following description taken in conjunction with the accompanying drawings in Which:

FIGURE 1 is a theoretical profile for detrital units with stationary shoreline and sand bar;

FIGURE 2 is a similar profile with a sand bar and shoreline moving toward a source area;

FIGURE 3 is a similar profile located below an unconformity under leaching conditions;

FIGURE 4 is a velocity log profile for five holes along a given traverse showing an Endicott sandstone section from Oklahoma; 7

FIGURE 5 is a velocity log profile showing Tonkawa sandstone in Oklahoma in the same holes as in FIGURE 4;

FIGURE 6 illustrates a system for generating conditions indicative of forces and movements present during the building of the sandstone beds of FIGURES 4 and 5;

FIGURE 6a is a more detailed circuit diagram of one of the storage units in the storage bank 66 of FIGURE 6.

FIGURE 7 is a structure contour map of the top of the Endicott sandstone over the area covered by the profile of FIGURE 4;

FIGURE 8 is an isopach map of the same area as FIGURE 7;

FIGURE 9 is an average porosity 'map of Endicott sandstone from data produced in FIGURE 6 for the same area as in FIGURE 7;

FIGURE 10 is an arithmetic deviation map of the porosity in the Endicott sandstone;

FIGURE 11 is a plot of center of gravity of the Endicott sandstone for the same area as in FIGURE 7;

FIGURE 12 is a structure contour map of the top of the Tonkawa sandstone over the area covered by the profile of FIGURE 5;

FIGURE 13 is an isopach map of the same area as FIGURE 12;

FIGURE 14 is an average porosity map of Tonkawa sandstone from data produced in FIGURE 6 for the same area as in FIGURE 12;

FIGURE 15 is an arithmetic deviation map of the porosity in the Tonkawa sandstone;

FIGURE 16 is a plot of center of gravity of the Tonkawa sandstone for the same area as in FIGURE 12;

FIGURE 17 is a summary set of profiles for the data of FIGURES 7-11 along the line X-Y taken therethrough; and

FIGURE 18 is a summary set of profiles for the data taken along the line PQ of FIGURES 12-16.

In order to understand the present invention, it will be helpful to consider briefly the conditions which, in the origin of a given subterranean body, affect the structural features thereof, such as the porosity. The factors which are primary in their effect on porosity and the corresponding geologic agents or conditions responsible for them are as set out in Table I.

TABLE I.--FACTORS AFFECTING PRIMARY POROSITY Factor Geologic Condition or Agent 1. Grain size Distance from source; depositional environment, energy level of environment.

2. Sorting Wave action; energy level of environment.

3. Grain geometry--. Source material; distance from source energy level of environment.

4. Cementation Percolating waters. (This can either by preor post-lithification).

5. Compaction overburden pressure and/or tangential pressure. (Mainly post-lithitlcation).

TABLE II.FACTORS INFLUENCING SECONDARY POROSITY Factor Geologic Condition or Agent 6. Cemeutation Percfilating waters.

7. Leaching o.

8. Jointing--. Consolidation contraction; tectonic itresses; mineralogical changes; rock- 9. Fracturing Tectonic stresses; rock-type.

10. Compaction -s overburden pressure; tectonic stress.

11. Mineralogical changes Percolating waters; overburden pressure; tectonic stress; temperature.

Of the factors listed above, it would appear that the grain size, sorting, grain geometry, cementation, and leaching are the most important contributors to porosity variations.

Examination of these factors in terms of geology reveals that the following geological agents or conditions are primarily responsible:

(a) Distance from source area;

(b) Depositional environment and energy level of environment;

(c) Percolating waters.

For any given area with marine sediments it may be said that the distance of the source area can be expressed as a simple function and that consequently the porosity changes due to this condition should be expressed by simple contour patterns. The energy environment, a factor that assumes more and more importance in the eyes of the exploration geologist, may change rapidly and in a complex manner. These changes then lead to local anomalies in the porosities changes and their proper interpretation can lead the favorable areas of hydrocarbon accumulation.

The third and in many cases the most important factor influencing porosity changes is the action of percolating waters. The changes can either be in a positive sense (increase of the original pore space) or negative sense (decrease of the original pore space).

Porosity changes in a positive sense are the result of percolating waters leaching out the more soluble constituents of the rock; whereas changes in a negative sense are effected by percolating waters depositing material in the original pore space.

Percolating waters are to a large extent a near-surface phenomena; consequently, porosity changes due to percolating waters in sedimentary rocks now buried under a considerable thickness of younger strata had to be at one time or other close to the surface after lithification.

The proximity to the surface of indurated rocks in turn can signify the presence of geologic unconformities in the stratigraphic column.

It has been found that maps portraying selected functions of porosity changes lead to a wholly new and most useful interpretation of the structural features of the subsurface formations. They lead to a more detailed knowledge of the geologic history of the area or basin in which the body of interest is found and thus permit more successful exploration for minerals such as hydrocarbons.

As an example, the conditions set forth in FIGURES 1-3 illustrate several geological possibilities which give rise to porosity anomalies the origin of which, in accordance with the present invention, can be delineated.

In FIGURE 1 there is illustrated the condition wherein a sand bar, now buried substantially within the stratigraphic column, was, during its formation, stationary in the sense that the bar grew in height as an accumulation of debris was deposited at that site without lateral change in the location of the predominant characteristics of the bar such as its crown and its axis. In the formation of such structures, it can readily be postulated that the energy level of the wave action would be high over the sand bar itself as well as at the shoreline. Thus, an energy level curve has been postulated in FIGURE 1 representing the variation in the energy of the formation forming forces. In such an environment the sorting and rounding of individual grains will be understood to be more thorough than in environments where the energy level is lower. Consequently, the values of porosity and the magnitude of deviation from an average porosity will be indicative of areas of high energy. Furthermore, if the bar should remain stationary during the period of its formation, its center of gravity should be found at the middle of the section thereof. Thus the two curves have been postulated for such a condition, the first being the arithmetic deviation from average porosity and the center of gravity of the section under consideration. By reason of the wave action during structure formation, the average porosity should show a regional decrease in porosity as one moves away from the source of the deposited debris such as at the shoreline. Thus, an average porosity curve has been illustrated, decreasing with distance away from the shoreline.

In FIGURE 2 there is illustrated a case in which it is postulated that a sand bar during formation moves progressively toward the source area, such as the shoreline. The theoretical profiles for such action and such structural activity are illustrated. Under ideal conditions the sand bar may be considered to move equal distances per unit of time. The momentary porosity anomaly will occupy each location along the line through which the section is taken in FIGURE 2, thus eliminating any porosity anomaly in any one location. The same considerations are true for the deviation function. During the accumulation the sand bar location will be present higher in the section than in any previous location. This condition may be detected by variations in the center of gravity which should have a decreasing depth in the section as the bar moves toward the source area or the shore line. The movement of the center of gravity, of course, is in the opposite direction in the case Where the sand bar undergoes regressive movement or movement away from the shoreline. In FIGURE 2 the energy level function, the average porosity function, the deviation function and the center of gravity function are postulated for the structural activity involved as the bar moves toward the shoreline.

In FIGURE 3 there is illustrated the condition wherein a detrital unit is positioned below an unconforrnity under leaching conditions. The postulated condition is that there is a slow and uniform transgression over a surface of erosion. The right-hand side of the figure will be covered with debris earlier with the younger sediments on the lefthand side of the figure being exposed for a longer period. Consequently, leaching will continue longer on the lefthand side which, in turn, will enlarge the original pore space to a greater extent. Under such conditions it could be postulated that the average porosity will increase in the direction of the transgression and thus, because of this, the deviation may be postulated as an increasing function in the direction of transgression. Further, since the leaching will be predominantly in the higher part of the section, the center of gravity will be above the center of the section and the values of the center of gravity function will decrease in the direction of the transgression.

The foregoing examples have been given in order to provide a basis for understanding the acquisition and use of geophysical data to produce functions such as the deviation in porosity and the location in the section of the center of gravity. Both functions are particularly indicative of the character of action present during the building of given sections of interest. Further, an indication is obtained of the direction to proceed from stations of observation of geophysical data to locations where accumulation of hydrocarbons might be most likely to be encountered.

Thus, in accordance with the present invention, there is provided a function representative of the average porosity of a given section of a lithologic column in at least two laterally spaced zones. A further function representative of the deviation from average porosity for each of the locations is then registered in correlation with the locations of the two spaced apart points. Further, and in a preferred embodiment of the invention, there is also registered a third function representative of the position of the center of gravity of the section of interest. In a preferred mode of carrying out the invention, the foregoing parameters are derived from acoustic velocity logs of a plurality of boreholes at spaced points over a basin in which a given formation is encountered. Preferably, the sections to be studied will be sands in which the formations are controlled in their structural features by wave action during the period of their growth.

It is to be understood that other means exit'for determining porosity values. However, it has been found that acoustic velocity logs are less susceptible to error than other logs and therefore would be preferred. Radioactivity logs and electrical logs are characteristic of the latter type.

Referring now to FIGURE 4, five velocity logs are illustrated for a section known as the Endicott sandstone as encountered in one part of the State of Oklahoma. Log was obtained in a first borehole A. That portion of the log covering the Endicott sandstone has been shown in detail. The log represents the incremental travel time for an acoustic wave to travel through a predetermined length or section of the sandstone bed. The log is of the type produced by systems such as disclosed in Patent No. 2,704,364 of Robert A. Broding, a co-worker of applicant. A second log 10a is also plotted through the same sandstone section and represents the self-potential (S.P.) curve for the same section covered by the log 10. A similar acoustic velocity log 11 and an S.P. log 11a are illustrated for the borehole B. Logs 12 and 12a similarly were obtained in borehole C. Logs 13 and 13a were obtained in borehole D. Logs 14 and 14a were obtained in borehole E. The location of the holes is best illustrated in FIGURE 7. They span a traverse covering five townships, the area shown in FIGURE 7 being five townships long and two townships wide. In the course of carrying out the present invention, similar logs were obtained for each of the remaining boreholes appearing in FIGURE 7. However, for the purpose of the present description, detailed consideration will be given only to those logs shown in FIGURE 4.

As previously explained, the velocity logs may be employed for the purpose of determining the porosity of certain formations of interest. The system illustrated in FIG- URE 6 is provided in accordance with the present invention to carry out, in analog form, the necessary treatment 6 of data represented by the logs of FIGURE 4 to provide porosity data.

More particularly, the system of FIGURE 6 provides a record, on a first trace 20, of a signal representative of the average porosity of the Endicott sandstone at each of the five wells. The first pulse 20a is representative of the average porosity in borehole A. Pulses 20b, 20c, 20d and 20e represent the average porosities in boreholes BE, respectively.

Further, a second trace 21 is produced which represents the deviation (preferably arithmetic) of porosity from average porosity for each of the holes. The trace 21 includes pulses 21a-21e which represent the deviation experienced or encountered at each of the boreholes A-E, respectively.

Fin-ally, a trace 22 is produced having scalar functions recorded thereon in the form of pulses 22a-22e representing the location of the center of gravity of the Endicott sandstone in each of the boreholes A-E, respectively.

Referring now to FIGURE 6, there is illustrated a photoelectric scanner 30 which includes a drum 31a for rotationally supporting a transparency 32. A motor 33 is provided to drive the drum 31a. A light source 34a directs a beam of light to a prism 34b which reflects the beam of light through the transparency 32 and through a light slit in a baffle unit 35. Light emerging from the unit 35 passes through a condensing lens 36 and impinges on a photocell 37. The output of the photocell passes through a preamplifier 38 to a stepping switch 39 by way of channel 39a. The photoelectric scanner 30 is employed for the purpose of generating on channel 39a an electrical signal corresponding with the data on the transparency 32. Of particular interest is that data lying within the segments 40 and 41. Additional transparencies on drums 31b, 31c (and two additional transparencies not shown) are to be employed in the production of the data on traces 20, 21 and 22. Data from four additional scanners is transmitted to the switch 39 by way of channels 3%- 39e, respectively.

The arm of the stepping switch 39 is controlled by relay coil 45 which is closed momentarily at the end of alternate cycles of scanning of a given transparency. More particularly, a cam 45a controls a switch in circuit with battery 45b for periodically energizing coil 45. The cam' 45a is coupled to the motor 33 by a linkage 33a. The motor 33 also drives the additional photoelectric scanners for the transparencies on drums 31b, 310, etc.

The arm of the stepping switch 39 is connected to a system which carries out the computations indicated by the following four equations.

A logA matrix A liquidA matrix Where 7p: average porosity,

=porosity at each depth along the formation, and

n=a depth function, increasing in direct proportion to depth.

where AD=arithmetic deviation and the remaining functions are as above identified with respect to Equation 2.

1 where:

C.G.=center of gravity of the formation, and h =distance from the top of the lithologic unit being studied to the middle of the interval for which is observed.

The center of gravity (C.G.) may be expressed in feet, but can be converted to percentage by dividing the distance from the top of the formation to the center of gravity by the thickness of the unit and multiplying by 100.

In order to produce the functions represented by Equations 1-4, the signal from the arm of switch 39 is applied to a first unit which carries out operations to produce the function of Equation 2. It will be assumed in the following description that the formation represnted by section 40 is to be detailed and that signals will be treated only from segment 40. The conductor 53 leading from the arm of switch 39 is connected to one input on the unit 50 which includes three sub-units 54, 56 and 58. Units 54 and 56 are identical units and produce an output function representative of the algebraic dilference between the two functions applied to the two inputs thereof. The channel 53 leads to one input of unit 54. The voltage on channel 53 is a varying DC. voltage the magnitude of which corresponds with the variations in the transparency 32 as in the section 40. A voltage source 55 is connected to the second input of both of the units 54 and 56. The voltage from unit 55 may be a steady D.C. voltage the magnitude of which is proportional to the incremental travel time for an acoustic wave to travel through a selected earth section wherein the earth section is made up solely of the matrix (the solids) at depths of the segment 40.

The voltage generator 57 applies to the first input of the unit 56 a steady DC. voltage the magnitude of which is proportional to the incremental travel time of acoustic pulse through the liquid in the same formation as encountered at the depth at section 40. The outputs of units 54 and 56 are then applied to a dividing unit 58. Thus, there is produced at the output terminal 59a a voltage which is a unidirectional voltage varying in amplitude with depth. The output voltage is representative of the porosity of the formation represented by the segment 40. The function appearing at terminal 59a is mathematically expressed by Equation 1.

It will be recognized that the voltages generated by units 55 and 57 will, to a considerable degree, control the magnitude of the porosity function appearing at terminal 59a. The present invention is not primarily concerned with determination of the values that are employed for the voltages from units 55 and 57. This, in general, is fairly well-known in the art and different investigators utilize different values for the matrix and liquid velocities. therefore, specific values for such velocities will be considered given.

Terminal 59a is connected by conductor 60 to the arm of a multichannel stepping switch 61. The stepping switch 61 is connected by way of linkage 33a to the motor 33 so that the arm of switch 61 will sweep all of the terminals of FIGURE 6 during the time interval occupied by the selected segment of interest on the transparency on drum 31a. For example, the arm of switch 61 will be driven successively into contact with each of its terminals during the time interval represented by the segment 40. The linkage 33a is also connected to a voltage generator 63 which produces an output of stepped waveform which changes as the position of the arm of switch 61 changes.

The latter two functions are employed for producing an output function on line 64 which is representative of the average porosity over the section 40. As the arm of switch 61 sweeps its contacts, there are successively stored in the storage unit 66 electrical quantities each representative of the values of the porosity (p, at the various depths through section 40.

The storage device 66 may, for example, include a plurality of circuits each of the type shown in FIGURE 6A. The voltage from terminal 59a is applied by switch 61 to a rectifier 70 and a resistor 71 to place a charge on a condenser 72 proportional to the magnitude of the porosity at one depth in section 40. The voltage on the condenser 72 is then connected by way of a buffer device, such as a cathode follower 73, to an adding network 74. The sum of all of the voltages stored in unit 66 is then applied by way of channel 75 to the input of a dividing unit 76. The voltage on channel 75 is proportional to the summation of all of the porosity values 5 for the points in the segment 40 represented by the terminals on the switch 61. This voltage is then divided in unit 76 by a voltage proportional to or representative of the number of terminals of switch 61. The latter voltage is produced by generator 63.

As a consequence, there is produced on the output channel 64 a voltage representative of the average porosity of the formation represented by the segment 40. This voltage is then applied to a recorder 78 where the signal is recorded in the form of a pulse 20a on trace 20.

The pulse 20a is recorded during the first cycle of operation of the scanner 30 and the switch 61. Preparatory to the second cycle of the switch 61, the switch 69, FIG- URE 6A, in each of the storage units of the unit 66 will be switched to a playback position, as in contact with terminal 69a, so that the successive values of 1), stored in unit 66 will appear on the arm of switch 61. Further preparatory to the second cycle, the switch 59 is moved to the lower terminal 59b so that the successive values of will be applied to conductors 80 and 81. The values of (p produced on playback are employed to provide output functions which are respectively representative of the arithmetic deviation (AD) of porosity and the center of gravity (C.G.).

More particularly, in order to produce a physical representation of arithmetic deviation of porosity, there is provided first a subtraction unit 83 to which the average porosity function 5 on conductor 64 is applied. Subtracted from this are the successive values of as applied to unit 83 by way of conductor 80. The difference between the average porosity function and the functions is then applied to .a storage unit 84 by way of a multiterminal stepping switch 85. Switch 85 is driven in synchronism with switch 61, as indicated, by linkage 85a. The storage unit 84 is of the character of the storage unit 66 as above described. The output of the storage unit 84 is summed in a summing unit 86. The output of the summing unit 86 is then applied to a dividing unit 87, the denominator of which is proportional to the summation from 1 to n of 5 minus For this purpose the output of the generator 63 is applied as the denominator in the unit 87 as by way of the conductor 63b. The quotient function then appears on conductor 88 and represents the arithmetic deviation of porosity (AD). The value of the arithmetic deviation is recorded as pulse 21a on trace 21.

Simultaneously with the production of the arithmetic deviation function, there is also produced a function representative of the center of gravity (C.G.). This is produced by applying to a multiplier unit 90 a voltage on conductor 81 which represents the values as from storage unit 66. The product of such values and a depth function as produced by a potentiometer 91 is then applied to a multiterminal stepping switch 92. The potentiometer 91 and switch 92 are driven in synchronism with switch 61. A source 93 is connected across the potentiometer so that a voltage is generated which is proportional to the depth of a given function. The product of each function and its depth is then stored in a storage unit 94 of the same character as storage unit 66. A summing unit 95 is then employed toproduce on output conductor 96 a voltage which represents the summation of the products of the porosities and depths. The output conductor 96 is then connected to a dividing unit 97 as the numerator function. The denominator function is the same voltage as appears at the output of the summation unit 74. Conductor 75 is connected by way of conductor 75a to the second terminal of the dividing unit 97. The function produced on the output conductor 98 leading from the dividing unit 97 is then the center of gravity (C.G.) function for the section 40. The conductor 98 is connected to the third input terminal of the recorder 78 to record as pulse 22a the center of gravity function on trace 22. The pulses 20a, 21a and 2211 thus represent the solutions for the formation represented by the segment 40 of the three Equations 2, 3 and 4.

The foregoing operations are then repeated for each of the transparencies on drums 31b, 31c and two additional transparencies (not shown) for the production of the pulses 20b, 21b, 22b, and the remaining pulses on the lower record section 40. The recording 40' is a regis tration of new and distinctive geophysical functions descriptive of the formation as represented by the segment 40.

. Thereafter there will be produced a similar recording 41 for the record section 41. Pulses 20f-20j of recording 41' represent the average porosity for the record section 41 at each of five wells. The pulses 21f-21j represent the deviation from average porosity. Pulses 22f- 22j represent the center of gravity functions.

The segments of sonic logs of FIGURE 4 represent the actual velocity logs for the Endicott sandstone in five wells A-E in a given section in Oklahoma. FIGURE 5 includes segments of the same logs as in FIGURE 4 but for a deeper, Tonkawa sandstone. The wells have been given the same reference characters A-E in FIGURES 4 and 5. The Endicott and Tonkawa formations have been employed in order to illustrate the application of the present invention to actual field problems. The data taken from such logs, recorded or registered in correlation with the locations of the different wells as on the record traces 20-22, may then be employed to provide further and more revealing information as to the character of the forces which were active during the period of time that the sandstone fomations in question were being built.

' More particularly, as illustrated in FIGURES 7-11, the data on the output of the recorder 78 may be employed to provide a new and informative picture of formation development and the direction which one might go from a given point of investigation to find locations more susceptible to entrapment and storage of petroleum accumulations. For example, the recorder 78 plots as scalar values the functions for each of the wells in which the logs are run. FIGURES 7-11 indicate the five different sets of functions all of which are related to the Endicott sandstone. FIGURE 7 is a srtucture contour map showing the top of the Endicott sandstone in the area in which holes A-E are located.

FIGURE 8 is an isopach map of the Endicott sandstone over the area covered by the wells A-E.

The values of trace 20a are plotted as to form an average porosity map such as shown in FIGURE 9. It will be noted that there are many wells from which data was gathered other than the wells A-E. As a result of the values found on trace 20, the average porosity can be contoured to form the various contours shown in FIG- URE 9.

In a similar manner, the values shown on trace 21 are plotted in FIGURE 10 and from this contours are drawn showing the arithmetic deviation from average porosity.

Finally, as illustrated in FIGURE 11, the values on trace 22 are plotted and the contours there drawn show the variations in the center of gravity for the Endicott sandstone.

While the values plotted and the contours shown may be carried out by hand, it will be recognized that automatic plotters and contouring devices may be employed for carrying out the actual construction of the maps of FIGURES 9-11.

FIGURES 12-16 comprise a similar family of maps corresponding respectively to FIGURES 7-11 but in which the data represents the Tonkawa formation. It will be noted that there are substantial differences in the contours shown and, further, it will be appreciated that only a limited area has been plotted in the maps of FIG- URES 7-16. Even so, the principle of the present invention is clearly illustrated. More particularly,v by striking a line such as the line X-Y across the maps of FIGURES 7-11, there may be obtained the data for plotting the five curves shown in FIGURE 17. The curve represents the center of gravity of the Endicott sandstone as it occurs along the line X-Y, FIGURE 11. The line 101 represents the arithmetic deviation from average porosity along line X-Y, FIGURE 10. The curve 102 represents variations in average porosity along the line X-Y, FIGURE 9. The curves 103- and 104 respectively represent variations as taken from the isopach map of FIGURE 8 and the structure map of FIGURE 7.

The curves 100-104 correspond in essence to the five curves shown in FIGURE 1. The hypothesis upon which the FIGURES 1-3 was based may then be applied directly to the curves of FIGURE 17 to determine the nature of the forces present during the time the Endicott sandstone for-mation was being laid down. One can then construct additional graphs such as that of FIGURE 17 as taken along different lines to locate the areas in which there is greatest porosity and in which functions of arithmetic deviation of porosity and center of gravity will indicate the zones most likely to be reservoirs of hydrocar bon accumulations.

In FIGURE 18 there is shown a similar set of curves including curves 110, 111, 112, 113 and 1'14 for the Tonkawa sandstone. The curves correspond with the center of gravity deviation, average porosity, isopach and structure of the Tonkawa sandstone as taken along lines P-Q of the FIGURES 12-16. Curves -114 correspond to those functions illustrated in FIGURES 1-3 and are to 'be interpreted on the basis proposed for FIG- URES l-3. The utility of the present invention is graphically shown by the use to which the newly developed data may be put, as in contours of the type shown in FIG- URES 7-16.

The foregoing description has dealt primarily with the use of an analog system such as shown in FIGURE 6 for carrying out the present invention. It will be understood that the method may be practiced through use of systems other than analogs of the type above described in detail. More particularly, each operation embodied in the production of a deviation function and a center of gravity function, as well as the average porosity function, may be carried out through the use of the more flexible and versatile digital computers. The method, therefore, is not limited to the particular form of analog apparatus disclosed herein, nor to any particular analog system. Nor is the method limited to the production of.

the particular functions above described. Porosity may be derived from logs other than the velocity function. Even when based upon the velocity function, a different relationship may be employed other than embodied in Equation 1. Similarly, while Equation 3 specifies a deviation that is a simple arithmetic function, other deviation functions may be considered by some persons'skilled in the art to present a more exact picture than the function employed herein as exemplary only. In any case, there is provided a new method of carrying out geophysical exploration. A new and interpretative set of geological data is provided which is highly useful.

The system at FIGURE 6 includes in block form a number of components which, in general, are well-known in the art and for this reason are not shown in detail. For example, the subtraction units 54, 56 and 83 may be of the type described in Waveforms, Radiation Laboratory Series, volume 93, McGraw-Hill (1947) in the section entitled Addition and Subtraction of Voltages and Currents, page 629. A suitable subtraction unit is described at page 642 under the heading Cathode Coupling. Summing units are also disclosed in the same section. A suitable network is shown in Figure 18.1 at page 631 of the above reference. Dividing networks 58, 76, 87 and 97 may be as described in the section entitled Multiplication and Division in the above-identified reference. Multiplying networks such as employed in the circuit of Figure 19.1 of the above reference may be of the type disclosed in Patent 2,982,942 to J. E. White. The voltage generator 63 may be of the type described under the heading Linear Steps of Voltage beginning at page 617 of Waveforms which describes several types of voltage generators having stepped output functions. A trigger voltage supplied to this circuit in coincidence with each step of the switch 61 provides the synchronism for the output voltage. A direct linkage has been indicated from the relay coil 4-5 to the recorder drive for the recorder 78. It is to be understood that other drive means, such as well-known Selsyn systems, may be employed to coordinate or synchronize the motion of the recorder chart with the switch 39. Furthermore, the records 40' and 41' have been employed in the particular configuration shown in FIGURE 6 in order to graphically portray one form of presentation of the results of the present invention. It is to be understood that different forms of recording may be found perhaps more harmonious with the mode of end use than the form illustrated herein.

Thus, in accordance with the present invention, there is provided a new set of data relating to significant structural properties of earth formations. There is first produced a function representative of the average porosity of a given formation. Together with the foregoing function there is produced and recorded a function representative of the deviation of average porosity at various points throughout the section. Finally, there is recorded a function representative of the location of the center of gravity of a given formation. The functions are then recorded or registered in correlation with the location of the boreholes or the sites in which the various formations are encountered as on records 40 and 41'. From such records a new and useful interpretation is had as to the character of the formations encountered.

Having described the invention in connection with certain specific embodiments thereof, it is to be understood that further modifications may now suggest themselves to those skilled in the art and it is intended to cover such modifications as fall within the scope of the appended claims.

What is claimed is:

1. The method of determining the time-depositional changes during formation of a subterranean earth unit with respect to which variations in porosity as a function of depth within said unit are known for at least two spaced vertical lines extending through said unit, which comprises:

(a) generating a first pair of functions representative of said variations in porosity along said lines,

(b) generating a second pair of functions representative of the numerical value of the deviation from an average of said porosity functions along said lines, and

(c) registering each of said second pair of functions in correlation with the locations of said lines.

2. The method of determining time-depositional changes during formation of a subterranean earth unit with respect to which the variations in porosity as a function of depth within said unit are known for each of a plurality of spaced lines extending through said unit, which comprises:

(a) for each said line generating a function representative of the average porosity of said unit,

(b) modifying each of the average porosity functions to produce functions representative of the numerical value of the deviation from said average porosity function for each of said lines, and

(c) registering the deviation functions in correlation with the locations of said lines.

3. The method of determining the time-depositional Changes during the formation of a given subterranean earth unit, which comprises:

(a) generating a first set of functions representative of a physical variable of said unit controlled primarily by variations in porosity through said unit along all of a plurality of vertical lines extending through said formation at laterally spaced points,

(b) modifying said first set of functions to produce a second set of functions representative of the product of said variations and the depth points at which they occur along each of said lines through said unit,

(c) modifying said second set of functions to produce a third set of functions representative of the quotients of said second set of functions and the summations of porosities at said depths, and

(d) registering said third set of functions in correlation With the locations of said lines.

4. The method of determining the time-depositional changes during formation of a given subterranean earth 35 unit, which comprises:

(a) generating a first set of functions representative of a physical variable of said unit controlled primarily by variations in porosity through said unit along all of a plurality of vertical lines extending through said formation at laterally spaced points,

(b) modifying said first set of functions to produce a second set of functions representative of average porosities along said lines through said unit,

(0) establishing from said second set of functions a third set of functions representative of the numerical values of the deviations from the respective averages of the porosity over the thickness of said unit at each of said lines, and

(d) registering said third set of functions in correlation with the locations of said lines.

5. A system for well log interpretation which comprises:

(a) means to produce a first function which varies in accordance with variations in said log along a selected formation represented thereby,

(b) means for modifying said first function to produce a second function representative of the incremental formation porosity as it varies along said formation, and

(c) means responsive to said second function for generating a third function representative of the magnitude of the deviation in the porosity function from the average of said porosity function.

6. A system for well 10g interpretation which comprises:

(a) means to produce a first function which varies in accordance with variations in said log along a selected formation represented thereby,

(b) means for modifying said first function to produce a second function representative of the incremental formation porosity as it varies along said formation,

(0) means for generating a third function representative of the magnitude of the deviation in the porosity 13' function from the average of said porosity function, and

(d) means for recording said third function.

7. A system for well log interpretation which comprises:

(a) means to produce a first function which varies in accordance with variations in said log along a selected formation represented thereby, and

(b) means for modifying said first function to produce a second function representative of the distance from one boundary of said formation to the location of its center of gravity.

8. A system for well log interpretation which comprises:

(a) means to produce a first function which varies in accordance with variations in said log along a selected formation represented thereby,

(b) means for modifying said first function to produce a second function representative of the distance from one boundary of said formation to the location of its center of gravity, and

() means for recording said second function.

9. In Well logging interpretation where a function is produced which represents the magnitude of the porosity as it varies over a given formation represented on a well log, the combination which comprises:

(a) storage means for storing functions representative of the incremental porosity at each depth in a series of depth points extending across said formation,

(b) means for generating a function representative of the magnitude of the sum of said incremental po rosity functions,

(0) means for producing the quotient of said sum and the number of points in said series to produce an average porosity function for said formation, and

(d) means for recording said average porosity function.

10. In a well logging interpretation where a function is produced which represents the magnitude of the porosity as it varies over a given formation represented on a well log, the combination which comprises:

(a) storage means for storing functions representative of the incremental porosity at each depth in a series of depth points extending across said formation,

(b) means for generating a function representative of the magnitude of the sum of said incremental porosity functions,

(c) means for producing the quotient of said sum and the number of points in said series to produce an average porosity function for said formation,

(d) means for storing a plurality of functions each representative of the difference between said average porosity function and said incremental porosity function at each one point in said series,

(e) means for producing a function representative of the summation of absolute magnitude of all of the difference functions for all of said depth points,

(f) means for generating a function representative of the quotient of said summation and the number of said depth points to produce a deviation function, and

(g) means for recording said deviation function.

11. In well logging interpretation where a function is produced which represents the magnitude of the porosity as it varies over a (given formation represented on a well log, the combination which comprises:

(a) storage means for storing functions representative of the incremental porosity at each depth in a series of depth points extending across said formation,

(b) means for generating a function representative of the magnitude of the sum of said incremental porosity functions,

(-0) means for producing the quotient of said sum and the number of points in said series to produce an average porosity function for said formation,

(d) means for recording said average porosity function,

(e) means for storing a plurality of functions each representative of the difference between said average porosity function and said incremental porosity function at each one point in said series,

(f) means for producing a function representative of the summation of absolute magnitude of all of the difference functions for all of said depth points,

(g) means for generating a function representative of the quotient of said summation and the number of said depth points to produce a deviation function, and

(h) means for recording said deviation function.

12. In well logging interpretation where a function is produced which represents the magnitude of the porosity as it varies over a given formation represented on a Well log, the combination which comprises: i

(a) storage means for storing functions representative of the incremental porosity at each of a plurality of depth points extending across said formation,

(b) means for reproducing the stored functions in the :order of their depth occurrence,

(c) a multiplier means for producing the product of each of said stored functions and a function de pendent upon the depth of the formation having the given porosity function,

(d) storage means for storing each said product,

(e) means for producing a function representative of the sum of the stored products,

(f) means for generating the quotient of the sum of the stored products divided by the sum of said porosity functions, and

(g) means for recording said quotient as representative of the center of gravity of said formation.

13. In well log interpretation where incremental porosity functions are known for a given formation, the method which comprises:

(a) modifying the functions to produce a function C.G. in accordance with the relaitonship where:

AD is the arithmetic deviation, n is a depth function for each point along said formation having a function 5,, and

(b) registering said function AD.

15. A system for indicating the time-depositional changes during formation of a subterranean earth unit with respect to which variations in a porosity dependent log as a function of depth are known for a plurality of spaced vertical bores extending through said unit Which comprises:

(a) means for generating for each of said bores a first second function representative of the deviation from function representative of variations in porosity, an average of said porosity along said bores,

(b) means for generating for each of said bore a (c) means for generating a third function representasecond function representative of the deviation from tive of the distance from one boundary of said unit an average of said porosity along said bores, and 5 to the center of gravity thereof, and

(c) means for registering said first and second func- ((1) means for registering said first, second and third tions at points along a space scale representative of functions in correlation with the locations of said the distance between said bores. bores.

16. A system for indicating the time-depositional R f changes during formatlon of a subterranean earth unit 10 e erences Cited by the Exammer with respect to which variations in a porosity dependent UNITED STATES PATENTS log as a function of depth are known for a plurality of 3,147,458 9/1964 Wagner 340-155 spaced vertical bores extending through said unit which 3,175,639 3/1965 Libcn 340-18 X comprises: 3,180,141 4/1965 Alger 73152 (a) means for generating for each of said bores a first 15 function representative of variations in porosity, BENJAMIN BORCHELT, Primary Examiner- (b) means for generating for each of said bores a SKOLNIK, Assistant Examiner 

1. THE METHOD OF DETERMINING THE TIME-DEPOSITIONAL CHANGES DURING FORMATION OF A SUBTERRANEAN EARTH UNIT WITH RESPECT TO WHICH VARIATIONS IN POROSITY AS A FUNCTION OF DEPTH WITHIN SAID UNIT ARE KNOWN FOR AT LEAST TWO SPACED VERTICAL LINES EXTENDING THROUGH SAID UNIT, WHICH COMPRISES: (A) GENERATING A FIRST PAIR OF FUNCTIONS REPRESENTATIVE OF SAID VARIATIONS IN POROSITY ALONG SAID LINES, (B) GENERATING A SECOND PAIR OF FUNCTIONS REPRESENTATIVE OF THE NUMERICAL VALUE OF THE DEVIATION FROM AN AVERAGE OF SAID POROSITY FUNCTIONS ALONG SAID LINES, AND (C) REGISTERING EACH OF SAID SECOND PAIR OF FUNCTIONS IN CORRELATION WITH THE LOCATIONS OF SAID LINES. 